I'm still concerned about the black vs white heat emission issue. The photochem and energy transport phenomena don't change on the 'outbound' side for white vs black. Perhaps the kinetics will change - but that wasn't part of the discussion before. And yes, the heat transport phenomenon will definitely be tied to the material, surface structure, etc. - I agree on those points that others have raised. But, those points are in agreement with my original point, not in opposition - the variable of concern for out 'other' category is NOT color, but material! Color becomes an issue when determining the energy in, not the energy out.
People are getting caught up on the issue of a blackbody vs whitebody. They will both emit light from the 'blackbody' process based on temperature, not color. Remember that the terms 'blackbody' and 'whitebody' are tied to thepractical experimental side that led to the fundamental measurements.. All objects will have both blackbody (emittive) and whitebody (reflective/scattering) behavior in different proportions. Perhaps I was not careful enough in setting that up in my earlier post. In the end, the albedo differences some pointed out are tied to the reflective/scattering behavior generally 'drowns' out and blackbody components. So I are that a low albedo is preferable for a 'spy' satellite (and the sort), but that has to be balanced against the light absorption heating.
So, the discussion is a tangent from the original point - the whatever-paint-body will lose a small amount of thermal energy by emission of a photon. This process will likely be slower than the rate of absorbed photons in all cases I can imagine for an orbiting body (unless perhaps it's parked in the shadow of a planetary body - then we'd need numbers for Mie scattered light around the planet, etc. But now we're really running afield.) So:
energy out - independent of paint color
energy in - minimized for low absorptivities (i.e. white or reflective)
So, if you're minimizing solar heating for an orbiting body, black is a poor choice. When you begin balancing this against detectability, you have a more multivariate problem. But even there, I would aim for a high reflectivity approach that is directional, and directed away from potential observers. Or (in the ideal world where we do not live) for 100% efficiency solar panels (in the realistic world, perhaps a transformation of the light into something mostly other than heat can still thread the needle. Again, tangential.)
For my money, I'm going for a surface that's highly reflective but highly directional, and I'd pont is somewhere I never expected an observer. Better yet, I'd have an umbrella (black) set up in that direction in case an observer ever was there. And, while I'm wish listing, I'll put that high efficiency solar converter at this point, to further mask the 'beam' reflected and turn it into useful power, that doesn't heat the real satellite (so we want a tether with minimal heat transfer.)
(Merry Christmas all, the outline for a DARPA grant - if it hasn't already been done.)